Question

4. (10 points) Write a computer code to compute the unit roundoff error (machine epsilon) on a given machine using double precision. You need to compute the smallest positive machine number є such that 1 + є I. (Hint: You can divide the number 1 by 2 repeatedly, each time the division is equivalent to adding a zero before the binary point.) The computer computed machine epsilon number and the code has to be attached to your homework.

Please write in C or C++, professor said it's supposed to be pretty short, like 10 lines, if that helps.  

I also need to have a check for an infinite loop. Thanks in advance!

Answer 1

#include <stdio.h>

int main() {
   double e = 1;
   while(1+e != 1) {
      e /= 2;
   }
   printf("unit roundoff error is %.50lf\n", e);
   return 0;
}

unit roundoff error is 0.00000000000000011102230246251565404236316680908203